What is the equation of a line that is perpendicular to the line y = 2x + 4 and passes through the point (-2, 3)?

Answers

Answer 1

Answer:

[tex]y=-\frac{1}{2} x+2[/tex]

Step-by-step explanation:

The given equation is written in slope-intercept form:

[tex]y=mx+b[/tex]

where:

m is the slopeb is the y-interceptx and y are the corresponding coordinate points (x,y)

The slope is 2:

When two lines are perpendicular, their slopes will be opposite reciprocals. Find the slope of the line perpendicular to the given equation:

[tex]m_{1}=2[/tex]

This can be seen as:

[tex]m_{1}=\frac{2}{1}[/tex]

Flip the fraction (reciprocal):

[tex]\frac{2}{1}[/tex] → [tex]\frac{1}{2}[/tex]

Now find the opposite:

[tex]\frac{1}{2}[/tex] → [tex]-\frac{1}{2}[/tex]

So the slope of the perpendicular line is:

[tex]m_{2}=-\frac{1}{2}[/tex]

Now make an equation written in point-slope form:

[tex]y-y_{1}=m(x-x_{1})[/tex]

where:

m is the slope[tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the corresponding coordinate points [tex](x_{1},y_{1})[/tex]

Insert information:

[tex]y-3=-\frac{1}{2} (x-(-2))\\\\y-3=-\frac{1}{2} (x+2)[/tex]

Simplify to slope-intercept form. Solve for y:

Use the distributive property:

[tex]y-3=-\frac{1}{2}(x)-\frac{1}{2} (2)\\\\ y-3=-\frac{1}{2} x-1[/tex]

Add 3 to both sides to isolate the variable:

[tex]y-3+3=-\frac{1}{2} x-1+3\\\\y=-\frac{1}{2} x+2[/tex]

:Done


Related Questions

Select all the true statements about the graph of a line that slants downward from left to right.

A The slope of the line is negative.
B As the value of one variable increases, the value of the other variable decreases.
C The slope of the line is a fraction.
D The graph of the line has extremely small values.

Answers

Answer:

A. The slope of the line is negative.

B. As the value of one variable increases, the value of the other variable decreases.

For C and D, the line that slants downwards from left to right can have these qualities, but not always. As for A and B, it will always have these qualities.

The true statements about the graph of a line that slants downward from left to right will be:

A. The slope of the line is negative.B. As the value of one variable increases, the value of the other variable decreases

It should be noted that a graph of a line that slants downward from left to right will have the slope of the line to be negative and as the value of one variable increases, the value of the other variable will reduce.

On the other hand, the slope of the line is not always a fraction and the graph of the line doesn't have to possess small values.

Read related link on:

https://brainly.com/question/17738017

Willie won 125 lollipops playing hoops at
his school's game night. Later, he gave
four to each of his friends. He only has 1
remaining. How many friends does he
have?

Answers

Answer:

Step-by-step explanation:

Easiest way to do this is to work backwards.

If Willie only has 1 remaining lollipop, this means that he must've given a total of 124 lollipops to his friends.  (125 - 1 = 124)

Then we know he gave 4 lollipops to each friend. So all you need to do is divide the total number of lollipops he gave to his friends (124) by how many he gave to each friend.

Number of friends = Total number of lollipops given to friends / Number of lollipops given to each friend.

Number of friends = [tex]\frac{124}{4} = ?[/tex]

Jayden starts with $1575 in a college savings account. His account earns interest at a rate of 2.7% compounded annually. How much money is in the account after 9 years?

Answers

Step-by-step explanation:

2.7/100*1575=42.525

then for 9years

9*42.525=$382.725

*
Convert 499 m to km
499,000 km
O 0.499 km
49.9 km
0 4.9 X 10^-3 km

Answers

Answer:

the answer is 0.499 km I also used a calulator to double check.

I missed my zoom lesson today and I don't understand the material we covered. I'm not sure how to answer this question. Thank you in advance for your help ​

Answers

Answer:

True

Step-by-step explanation:

Skew lines are two lines that do not intersect and are not parallel.

AB and CG are neither intersecting nor parallel. So, they are skew lines.

Hope it helps:)

Simplify 6.92⁰.

A. −1

B. 0

C. 1

D. 9.92

PLZZZZZ HELP I WILL MARK BRAINLIEST IF IT IS RIGHT AND MUST HAVE AN EXPLANATION

Answers

Answer:

0

Step-by-step explanation:

ANYTHING TIMES ZERO IS ZERO.

THERE ISN'T ANY 6.92. IT'S JUST ZERO

what is the distance between -4 and 6 in units

Answers

the distance between -4 and 6 in units is 10

What is 3,763 divided by 6

Answers

Answer:

627.166666667

rounded is 627.17

NOW ANSWER THE QUESTION THIS TIME

Answers

Answer:

60 – 80 pounds, while a trophy can weigh over 100 pounds

1.4–1.8 kg (3.1–4.0 lb) and a fork length of 60 cm (24 in). At age seven, females average 10 kg (22 lb), males 5 kg (11 lb). King mackerel may attain 40 kg (88 lb), but any over 7 kg (15 lb) is almost certainly a female.

blue marlin 210 lbs

black marlin 1,650 lb

white marlins approximately 180

100 pounds.

For the function H(t) = 3t - 5
Find when H(t) = 46

Answers

Answer:

t = 17

Step-by-step explanation:

Plug in 46 for H(t) into the above equation and solve for t.

46 = 3t - 5 (add 5 to both sides)

51 = 3t (divide both sides by 3 to isolate t)

17 = t or t = 17

Can someone help please :)
The least common multiple of 54 c^2 de^3 and 38 c^4 is _____.


A. 1,026 c^4
B. 342 c^4 de^3
C. 342 c^2
D. 1,026 c^4 de^3

Answers


The correct answer is 1,026 c^4 de^3.

Explanation: 1,026 is the lowest number both 38 and 54 go into. c^4 is the lowest that both go into. de^3 is also the lowest they all go into since de^3 is only in the first equation.

Answer:

The correct answer is 1,026 c^4 de^3.

Step-by-step explanation:

Given the function g defined by the formula g(x) =x − 5/2x-5 find the following:

Answers

gksiabfjc sajtifnxwnwjriv end

Victor borrowed $19.50 from his mother to go to the theater. A week later, he paid her
$19.50 back. How much does he still owe her?
He owes her $

Answers

Answer: $0

Step-by-step explanation:

He paid her back the full amount already so he doesn’t owe anything

Answer:

$0 right?

Step-by-step explanation:

If he borrowed $19.50 and gave her $19.50 back he would owe her $0

question in the image

Answers

Answer: 1

A shape will have a line of symmetry if it can be split in half and look exactly the same except reflected on both sides. For example, a butterfly has one line of symmetry.

This shape only has 1 line of symmetry, because there is only one way we can split it in half and still have it look exactly the same.

I hope this helps! Please comment if you have any questions.

The number of laps Jessica runs around the track is proportional to the times she spends running. She runs 12 laps in 1/2 hour. What is the constant of proportionality for the relationship between number of laps and number of hours

Answers

Answer:

6

Step-by-step explanation:

could someone please answer these 3 questions?? ty :))

Answers

Answer:

1. -12     2. you get -      3.  -6

Step-by-step explanation:

Well hope that makes sense. Please heart.

12 plus -12 is 0. -3 plus 2 is -1 or -.      -4 plus -2 is -6.

You add -12 to 12 to make it zero.

If you have - - -  and add  +  +  you get  -1.

If you have - - - -  and add - -  you get -6.

I really need help rn I got 5 mins left

Answers

What number do you need help with?

Joel’s veterinarian tells him that he can give his dog 11 5/8 mg of Benadryl for relief of his dogs allergies. Joel’s dog weighs 15 1/2 pounds.

Part a: what is the Benadryl dosage per pound for Joel’s dog?


Part b: If Joel’s veterinarian always uses the same milligrams per pound for prescribing aspirin to dogs, what would she prescribe for a dog that weighs 12 pounds?

Answers

Step-by-step explanation:

Given that,

The dosage of Benadryl for Dog is [tex]11\dfrac{5}{8}\ mg[/tex]

Weight of Joel's Dog is [tex]15\dfrac{1}{2}\ \text{pounds}[/tex]

(a)  Benadryl dosage per pound for Joel’s dog is calculated as :

[tex]\dfrac{11\dfrac{5}{8}}{15\dfrac{1}{2}}=\dfrac{\dfrac{11\times 8+5}{8}}{\dfrac{15\times 2+1}{2}}\\\\=\dfrac{\dfrac{93}{8}}{\dfrac{31}{2}}\\\\=\dfrac{93}{8}\times \dfrac{2}{31}\\\\=0.75\ \text{dosage per pound}[/tex]

(b) If the weight of the Dog is 12 pounds, it means

[tex]\dfrac{11\dfrac{5}{8}}{12}\ \text{dosage per pounds}\\\\=\dfrac{\dfrac{93}{8}}{12}\\\\=\dfrac{93}{8}\times \dfrac{1}{12}\\\\=0.968\ \text{dosage per pounds}[/tex]

Therefore, this is the required solution.

Jocelyn bought 18 chicken wings for $9. What was the cost of the wings in wings per
dollar?

Answers

18 wings = 9$
divide by eighteen
1 wing = 1/2 $

1/2 $ = 0.5 $

answer is 0.5 $ or 50 c per wing

Answer:

Step-by-step explanation: 18 wings = 9$

divide by eighteen

1 wing = 1/2 $

1/2 $ = 0.5 $

answer is 0.5 $ or 50 c per wing

During the summer season, a jet ski rental company charges a 12% registration fee to reserve a jet ski that
rents for $90. How much is the fee?

Answers

Answer:

$10.80

Step-by-step explanation:

90*0.12=10.8

You start at (3,-2). You move down 1 unit and up 3 units. Where do you end?

Answers

Answer:

3,0

Step-by-step explanation:

The y coordinate goes down one unit to -3, then up 3 units to 0.

please help me, ASAP​

Answers

Answer:

The answer is A

Step-by-step explanation:

All of the other relations shows have duplicate numbers of x. For example, relation B has two 3s and D has two 20s. If a relation has a duplicate x, it is not a function.

Mr. Lee had 45 friction books. He gave 2 books to each
student. He has 1 remaining book. How many students does he
have?

Answers

Answer:

He has 22 students

Step-by-step explanation:

45 divided by 2 is 22 with 1 left over

Which expression is equivalent to 18 - 7?
A. -18 + 7
B. 18+ (-7)
C. 18 + 7
D. -18 +(-7)

Answers

Answer:

B

Step-by-step explanation:

The Equivalent Expression is 18+ (-7)

What are Integers?

Integers come in three types:

Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)

Given:

18 - 7

Using Integers

a- b can be written as a+ (-b)

So, 18 - 7

= 18+ (-7)

Hence, the Equivalent Expression is 18+ (-7)

Learn more about Integers here:

https://brainly.com/question/15276410

#SPJ2

Who is in charge or interacting with actors and technicians?

House Manager
Stage Manager

Answers

I think it could be the stage manager

Mr. Thomas drove from Banesville to Tempe and back.
How many miles did he save driving this route instead of driving
from Banesville to Georgetown to Tempe and back the same way?




Please HELP

Answers

Answer:

what are the answer options

Step-by-step explanation:

What are the next two numbers in the sequence?
4, 16, 64, 256,

Answers

Answer:

1024.

Step-by-step explanation:

You just multiply by 4

Perform the indicated operation.

11(-2)

22
9
-9
-22

Answers

Answer:

-22

Step-by-step explanation:

When you multiply a positive and negative number together, it becomes negative.

Multiplication is repetitive addition.

11(-2) = -11 + -11 = -22

plz help asap im being timed and i only have 20 minutes left

Answers

Answer:

first question is B

second F

third C

fourth pretty sure its C

last C

Step-by-step explanation:

A water cooler holds 15 liters of sports drink. Approximately how many gallons is this? (1 gallon = 3.785 liters)

Answers

Approximately 3.9 gallons I’m sure of

3 gallons

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